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  • A nonlinear eigenvalue problem with ▫$p(x)$▫-growth and generalized Robin boundary value condition
    Rǎdulescu, Vicenţiu, 1958- ; Saiedinezhad, Somayeh
    We are concerned with the study of the following nonlinear eigenvalue problem with Robin boundary condition ▫$$\begin{cases} -\text{div}(a(x, \nabla u)) = \lambda b(x,u) & \text{in} \quad \Omega \\ ... \frac{\partial A}{\partial n} +\beta(x) c(x, u) = 0 & \text{on} \quad \partial \Omega \end{cases}$$▫ The abstract setting involves Sobolev spaces with variable exponent. The main result of the present paper establishes a sufficient condition for the existence of an unbounded sequence of eigenvalues. Our arguments strongly rely on the Lusternik-Schnirelmann principle. Finally, we focus to the following particular case, which is a ▫$p(x)$▫-Laplacian problem with several variable exponents: ▫$$\begin{cases} -\text{div}(a_0(x) |\nabla u|^{p(x)-2} \nabla u) = \lambda b_0(x) |u|^{q(x)-2} u & \text{in} \quad \Omega \\ |\nabla u|^{p(x)-2} \frac{\partial u}{\partial n} +\beta(x) |u|^{q(x)-2} u = 0 & \text{on} \quad \partial \Omega. \end{cases}$$▫ Combining variational arguments, we establish several properties of the eigenvalues family of this nonhomogeneous Robin problem.
    Vir: Communications on pure and applied analysis. - ISSN 1534-0392 (Vol. 17, no. 1, 2018, str. 39-52)
    Vrsta gradiva - članek, sestavni del ; neleposlovje za odrasle
    Leto - 2018
    Jezik - angleški
    COBISS.SI-ID - 18124889

    Povezava(-e):

    http://dx.doi.org/10.3934/cpaa.2018003
    https://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=14556
    DOI

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